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By Duk-Won Park, Syd S. Peng

For an adequate design of the shortwall face support, it is necessary to understand fully the support- roof interaction. A series of studies has been carried out at a shortwall panel to develop the methods of monitoring support resistance and determining load density of the chocks. Various aspects of applications, for improvement of chock design and understanding of roof conditions, are discussed.

Jan 1, 1981

By D. H. Trollope

In engineering in general, close agreement between theoretical predictions and structural performance is rare—this is particularly true in rock slopes. Since the complexity of natural arrangements makes exact theoretical solutions of associated structural problems almost impossible, the role of theory should be that of developing guides or markers to which observations and experience can be related. The author in this paper has outlined the results of a theoretical study of highly idealized models which represent both granular materials and jointed rock. Some important practical considerations result—especially in regard to horizontal stresses—when theory is compared with full-scale experience. In the field of engineering activity, specific examples of close agreement between theoretical prediction and structural performance are rare. Particularly is this so for the case of rock slopes, where, owing to the complexity of the natural arrangements, it is quixotic to expect exact theoretical solutions to the associated structural problems. The role of theory is rather that of developing signposts or guide rails to which observations and experience can be related. It is with this in mind that the present paper has been prepared; the author's aim has been to set out briefly the results of a theoretical study of highly idealized models which represent both granular materials and jointed rock. Despite the idealization of the problem, it will be seen that the theoretical conclusions are in accord with full-scale experience, particularly as far as horizontal stresses are concerned, and they point to some important practical considerations. CLASSIFICATION OF ROCK SLOPES At the risk of over-simplification, an attempt has been made to classify the problem of rock slopes into three broad categories with respect to internal stress systems. These are illustrated in Fig. 1. It is tacitly assumed in this classification that the strength of individual particles is very much greater than the interparticle strength whether the particles are the crystals of an igneous rock (Case I) or the blocks of Cases 2 and 3. The Homogeneous Monolith: This case is representative of uniform unjointed rock. Under relatively low stress conditions the internal stress system may approximate to that of an elastic body as given by Terzaghi.' It is more usual, however, for overall stability, to consider the material as a rigid plastic which yields in shear when S =C + c tan 4> where S is the shear yield stress, o is the normal stress on the surface of failure, and C and d are empirical constants according to the Mohr-Coulomb criterion of failure. Sokolovsky has recently developed, for the first time, a series of mathematical solutions to problems involvinga C, mass subject to self-weight. He demonstrates that for such a case a semi-arch (Fig. 2) is stable. A corollary of this argument is that for a true C, d material a curved overhanging slope is possible and such an observation may well aid field identification of these materials. The shape of the curved slope face is however directly dependent on the C-value, and from the long-term point of view this is a most difficult value to establish with any degree of confidence. It is customary to measure C and 0 in some form of shear test—usually a triaxial compression test—on core specimens sampled from the rock, and as far as the author is aware the present case is the only one in which, as far as overall stability is concerned, such tests are

Jan 1, 1961

By J. Russ, C. L. Clark

For many years attempts have been made to develop a laboratory test that would serve to indicate the proper temperatures to be used in the various hot-working applications to which metals may be subjected as they are being processed from the cast ingot to the desired finished products. That these attempts have not been very successful is indicated by the fact that most of the temperatures in use today in these operations have been developed over a period of years by trial and error. In other words, the selection of the proper temperatures for the hot-working of metals is generally an art rather than a science. Our knowledge with respect to the behavior of metals at elevated temperatures has been greatly extended during the past several years. While most of the work in this field has been done at proposed operating temperatures of equipment, rather than at processing or fabricating temperatures, one outstanding fact has been developed, which is applicable to the entire high-temperature range; that is, that the rate of deformation to which the metal is subjected is of the same order of importance as the temperature. The failure to properly recognize this fact has greatly retarded the development of a suitable laboratory test for determining hot-working temperatures. Influence of Rate of Deformation on High-temperature Properties It is not the intent of this paper to survey all the work that has been done On the effect of deformation rate On the properties of metals. The importance of this factor, however, was shown by Zay Jeffries' as early as 1919, when he called attention to the existence of the so-called equicohesive temperature and to the effect of certain factors on the location of this temperature' Fig. I is a diagrammatic sketch showing the effect of temperature On the relative strength of the crystals and grain boundaries and the type of fracture that will res depnding On the location of the test, or Or temperature with respect to the equicOhesive temperature. Since the type fracture varies, it also follows that at temperatures below the equicohesive temperature the major deformation occurs in the grains: while at temperatures above, the deformation results either from the movement of the grains with respect to each other or recrystallization of the strained material occurs almost instantaneously, producing new crystals at the fracture. As previously indicated, it is an established fact that the position of this equicohesive temperature for any given metal is dependent On the deformation rate' For example, in 0.15 per cent plain carbon steel the location of this temperature under

Jan 1, 1947

By C. L. Clark, J. Russ

For many years attempts have been made to develop a laboratory test that would serve to indicate the proper temperatures to be used in the various hot-working applications to which metals may be subjected as they are being processed from the cast ingot to the desired finished products. That these attempts have not been very successful is indicated by the fact that most of the temperatures in use today in these operations have been developed over a period of years by trial and error. In other words, the selection of the proper temperatures for the hot-working of metals is generally an art rather than a science. Our knowledge with respect to the behavior of metals at elevated temperatures has been greatly extended during the past several years. While most of the work in this field has been done at proposed operating temperatures of equipment, rather than at processing or fabricating temperatures, one outstanding fact has been developed, which is applicable to the entire high-temperature range; that is, that the rate of deformation to which the metal is subjected is of the same order of importance as the temperature. The failure to properly recognize this fact has greatly retarded the development of a suitable laboratory test for determining hot-working temperatures. Influence of Rate of Deformation on High-temperature Properties It is not the intent of this paper to survey all the work that has been done On the effect of deformation rate On the properties of metals. The importance of this factor, however, was shown by Zay Jeffries' as early as 1919, when he called attention to the existence of the so-called equicohesive temperature and to the effect of certain factors on the location of this temperature' Fig. I is a diagrammatic sketch showing the effect of temperature On the relative strength of the crystals and grain boundaries and the type of fracture that will res depnding On the location of the test, or Or temperature with respect to the equicOhesive temperature. Since the type fracture varies, it also follows that at temperatures below the equicohesive temperature the major deformation occurs in the grains: while at temperatures above, the deformation results either from the movement of the grains with respect to each other or recrystallization of the strained material occurs almost instantaneously, producing new crystals at the fracture. As previously indicated, it is an established fact that the position of this equicohesive temperature for any given metal is dependent On the deformation rate' For example, in 0.15 per cent plain carbon steel the location of this temperature under

Jan 1, 1947

By C. E. Mills

Studies of ground movement and subsidence resulting from mining operations cover a broad field. It is also a very important consideration and one that eventually affects nearly every mining operation of any extent. The damage to surface buildings, removal of mine surface plants and replacements of main hoisting shafts must reach an astounding expenditure were these cost figures available over a period of years. Were the subject one of mathematical formula and dependent only on the angle of draw of the walls or country rocks, the problem would be relatively simple. Consideration must be given to depth and extent of workings; structural conditions of the orebodies and enclosing country rock; physical properties of these same rocks, including schistosity, bedding, jointing, slips, dikes, faults, and other structural weaknesses. The method of mining, extent of openings, supporting pillars, and amount of moisture or water underground are other pertinent factors. With such a large number of variable factors, it is apparent that the subject of subsidence is one that must be based largely on experience and results at other mines where conditions are somewhat comparable. In presenting this paper, it is the intent to describe the progressive results of past ground movements at the United Verde, to bring out physical conditions largely responsible for this movement, but to refrain from theorizing on the ultimate extent of subsidence resulting from future mining operations. Geology and Structure1 The ore deposits of the United Verde are of the massive sulfide, schist-replacement type. A structural anticline formed by the intrusion of diorite between bedding planes of steeply dipping and severely folded greenstones and porphyry localized the deposit of sulfide. The mineralized zone is of great horizontal extent varying from 200,000 to 400,-000 sq. ft., and extends from the surface to the lowest levels at a steep dip of from 50° to 75. The irregular interfingering of the sulfide with

Jan 1, 1934

By T. F. Witherbee

In the sections, Figures 1, 2, and 3, are shown three crucibles that have been applied to substantially the same furnace, all the conditions having been the same except a variation of one foot of bosh, and a slight variation in the angle of the same. The bosh of No. 3 was originally the same as No. 2, the additional foot in diameter being the result of three months' cutting. Beginning with No. 1, which mas 5 feet 6 inches diameter, with tuyeres 5 feet 4 inches high, and cinder-tap four feet from bottom, great trouble was found in holding iron a proper length of time, four hours being the outside limit when working well, and two hours or less if working badly. "Break-outs" through the iron

Jan 1, 1880

I TOLD you above that you should save the melted material that you extracted by smelting the ore. In substance this is copper, lead, silver, and perhaps gold, but all are like substances mixed in one body without any distinction. Now if you wish to separate these and to reduce them to their pure qualities, it is necessary to proceed with each one according to its own methods. Now in this method of separating lead in order to extract the silver and gold from the copper, it is necessary to return to the smelting and to follow one of two methods.* The first is to smelt it again with the addition of lead or lead ore, and to make it all run through the channel into the large forehearth that was made in front of the blast furnace, and, as it cools off, proceed to remove layer by layer with the fork, as I told you before and as you did the first time, until the work lead is reached. Then you assay what you have extracted and see whether it contains silver. If you consider that it has enough per hundred to justify the expense, return it again to the smelting. Continue to do this until you have extracted all the unctuousness and the work lead still remains. If it contains little or no silver, you must be satisfied with your work; otherwise return it again to smelt, always accompanying it with lead or galena and do as you did the other times until it

Jan 1, 1942

By J. R. Hassemer, T. T. Chao, University of Georgia, K. C. Watts, R. F. Sanzolone

Secondary oxides of Fe-Mn have been used in mineral exploration from the time gossans were first recognized Since gossans are conspicuous features and are largely explored, it is necessary to look for more subtle indication of blind mineralization. Sampling materials used in these geochemical studies consist of secondary Fe-Mn oxide-rich products of hydrothermal mineralization, and "in situ" weathering found in fracture fillings-as selvages along joints and disseminations in host rock. These materials were selectively collected and studied in the Silver City mining region. Two independent sampling methods were compared. The difference in the sampling methods was mainly in the ways samples were obtained and processed. One method involved systematic sampling of fracture fillings and coatings from which secondary Fe and Mn oxides and associated trace elements were then selectively extracted by chemical methods. The second approach involved collection of composite stream sediments and physical extraction of Fe-Mn oxide materials by gold panning, bromoform concentration, and electromagnetic separation. The source of the Fe-Mn-rich materials in the stream sediments is considered to be fracture fillings and coatings that mechanically entered the drainage basins. Map distributions of the two-sample types were compared. Both methods showed generally supportive patterns of anomalous metal dispersion, although anomaly-to-background contrast seems better in joint coatings. Both were useful in distinguishing geochemical differences between mining districts in the region. For example, the Pinos Altos district may contain more hydrothermally-introduced iron than the Central district, whereas the Central district has lead and zinc enrichments that are less on the amount of iron enrichment than is the case in the Pinos Altos district. The methods were qualitatively compared relative to time, expense, and other advantages and disadvantages.

Jan 1, 1984

By J. P. Witherow

The plant of Messrs. Oliver Brothers and Phillips, the only one in operation until January, 1886, has not been available for any further experiments since those of Mr. R. W. Hunt, described in his paper on the subject, at the Chattanooga meeting. Continuous working has, however, led to important improvements in plant, and furnished valuable results in practice. The difference between the converter and plant of 1884, as illustrated in our Transactions, vol. xiii., p. 759 and following pages, and those of 1885, may be observed in Plates 1. and 11. accompanying this paper. Plate I. gives the elevation and plan, in half-section, of one of our latest 3-ton converters. Plate 11. gives a plan of the general arrangement of a plant adapted to turn out slabs, blooms, and billets for the general market. The letters on Plate I. refer to the following parts :

Jan 1, 1886

By E. T. Turkdogan, P. Grieveson

Experimental results are presented for the rate of solution of nitrogen in a iron in the temperature range 750° to 873°C and in 6 iron in the temperature range 1410° to 1470°C. It is shown that the rate controlling process is diffusion of nitrogen into the iron. The diffusiting of nitrogen in a and 6 iron is derived from the results, and the temperature dependence of the diffusivity is represented by the equation D = 7.8 x e- 18,900/RT sq cm per sec. The solubility of nitrogen in a and 6 iron, in equilibrium with 1 atm pressure of nitrogen, has been measured. Using these results and other available data, it is found that the variation of the logarithm of nitrogen solubility with the reciprocal of absolute temperature is nonlinear. In an Appendix, some results of Darken and Smith are presented for the rate of solution of nitrogen in iron using ammonia + hyidrogen mixtures. These data also support the view that diffudsion of nitrogen in iron is the rate-controlling process when ammonia + hydrogen mixtures are used. A considerable effort has been made to obtain data on the solubility1-5 and diffusivity of nitrogen in a iron6-l2 because an understanding of the effect of nitrogen on the properties of steel must be based on an accurate knowledge of the properties of nitrogen in pure iron. However, no information is available concerning the kinetics of solution of nitrogen in a and 6 iron. Recently the authors13 have investigated the rate-controlling mechanism operating in the kinetics of solution of nitrogen in y iron. This study was directed to determine the rate-controlling processes for similar reactions with a and 6 iron as well as to establish values for the solubility of nitrogen in equilibrium with nitrogen gas in a and a iron. EXPERIMENTAL The procedure used in experiments to determine the rate of solution in cylindrical iron rods was the same as that described in a previous communication.13 Ferrovac E grade iron used in all experiments contained the following impurities in weight percent: C, 0.005; Mn, 0.001; P, 0.002; S, 0.006; Si, 0.006; Ni, 0.025; Cr, 0.002; V, 0.004; W, 0.02; Mo, 0.01; Cu, 0.001; Co, 0.01; 0, 0.007. After cleaning the surface, the iron rods were treated in an atmosphere of purified hydrogen for 17 hr before the reacting gas was introduced for known experimental times. After quenching, the samples were sectioned radially and analyzed for nitrogen. In addition to experiments using rods, iron foils were used in the measurements of solution rates of nitrogen in a iron. The foils of two different thicknesses were prepared by cold rolling Ferrovac E grade iron cylindrical rod to 0.051 and 0.152 cm. Foil samples were used in a rectangular form 5 cm long and 1.25 cm wide. The specimens were thoroughly cleaned of surface oxide with fine emery cloth and degreased with carbon tetrachloride immediately before entry into the furnace. The experimental procedure was the same as that used in the study with rods. At the completion of an experiment, the foil samples of the nitrogenized iron were analyzed for nitrogen after discarding 0.3 cm from the perimeter of the specimen. Iron foils were nitrogenized and denitrogenized in the a and 6 range with a gas mixture of 95 pct N and 5 pct H for times varying from 5 min to 2 hr. Results obtained for the average composition of nitrogen in iron for these experiments are presented in Fig. 1. Prior to the denitrogenization experiments, the samples were saturated with nitrogen at 1000°C and 0.67 atm N, giving a uniform nitrogen concentration of 0.0204 pct. According to the known a-y phase boundary in the Fe-N system,14 this composition lies within the ferrite region at temperatures 750" to 850°C. Use of this initial nitrogen content insured that reaction occurred between the gas and a single solid phase, a iron. Examples of the results for the mean concentrations of nitrogen in cylindrical iron rods, 0.356 cm radius for both the a and 6 ranges are given in Fig. 2. Typical examples of the results obtained for the radial distributions of nitrogen in rods are presented in Fig. 3. It appears that the results for radial distributions can be extrapolated to constant surface compositions which agree with the equi-

Jan 1, 1964

By Edward F. Fitzhugh

QUANTITATIVE appraisal of the chances of finding various tonnages and grades of ore clarifies any exploratory development proposal. Ways are discussed of appraising chances in conformance with probability principles, and graphs are suggested to show tonnages, grades and the corresponding judged expectancies.

Jan 1, 1947

By John Birkinbine

Four meetings of the Institute have been held in the anthracite coal-fields of Pennsylvania, and excursioris into the district, in connection with meetings elsewhere, have familiarized our members with

Jan 1, 1892

By R. C. de Lange

An improved replica technique is developed for a nondestructive study of the nucleation and growth of fatigue cracks. Three different growth stages of a fatigue crack were observed. An initial stage of high growth rate is followed by a long period of very slow growth, until finally a third period of high growth rate leads to fracture. THE metal-fatigue process is of a very complex nature. The experimental approach towards fatigue is susceptible to many minor influences which, together with the unavoidable scatter in testing results, makes the interpretation a matter of extreme care. The generally accepted fact that, in a homogeneous material, the fatigue cracks start at a free surface indicates that surface studies may contri-but in an essential way to a better understanding of the fatigue mechanisms. Indeed metallographic observations of the fatigue phenomena have been very fruitful in the last decade. The study of extrusions, intrusions, and persistent slip bands has contributed much to the present knowledge of the early processes in fatigue.' The drawback of the current metallographic techniques lies in the fact, however, that either observations of fatigue phenomena had to be made in a destructive way after an only partly executed test or a sequence of observations on the same test bar was only possible on notched specimens.2 4 In both cases an uncertainty exists as to the nucleation and growth of the fatigue crack in an unnotched test bar, where the crack can start at any place of a large area and develops in a test bar, which is macroscopically

Jan 1, 1964

Safety and health are no longer secondary responsibilities but must be of paramount concern to every mining operation, according to Anthony J. Thompson, an attorney with Hamel, Park, McCabe & Saunders of Washington D.C. The Mine Safety and Health Administration (MSHA) forecasts an estimated 19,000 inspections during 1979, and the economic and psychological impact of these inspections may he significant. To illustrate his point Thompson reviewed the experiences of a relatively large operation during a recent MSHA visit. The inspector was on the premises for two months, issuing between 250 to 300 "significant and substantial" (s&s) citations. During the most intensive period, about one month in duration, the operation experienced a production loss estimated between 2500 to 3000 tons; an accident rate up 30% over the previous month and 20% over the same month in the preceding year; 100% of the safety director's and safety engi¬neer's time was devoted to the inspection; 50% of top level management's time; and 90% of the mid-level or front line supervisory's time.

Jan 11, 1979

By R. W. Raymond

R. W. Raymond, New York City: In his paper at the New York meeting (Trans., xix., 28), Mr. Ledyard described, among other mines, the Belmont, in the county of Peterboro, Ontario, the developments of which at that time indicated, though they did not, perhaps, completely demonstrate, a deposit of high-grade Bessemer magnetite of very great extent. Mr. Ledpard said that experts estimated the quantity of ore within 100 feet of the surface at 1,000,000 tons. But the precise data upon which this estimate was based were not furnished. We are all interested in the development of fresh supplies of Bessemer ores. I think nobody who knows how enormous is the demand can seriously fear that such deposits will be exploited too rapidly. On the other hand, I need not here enlarge on the fact that a considerable number of enterprises, in which American ironmasters have been more or less interested, for the development of Canadian iron-ore deposits, have been unsuccessful, more by reason of disappointment as to the quantity of the ore and the facilities for cheaply mining it on a large scale, than as to its quality. Of course, a Canadian nine supplying the American market is handicapped at present, to the extent of 75 cents per ton, by the duty on foreign iron-ore; but this would certainly not be prohibitory in the case of a deposit sufficiently large, rich, and accessible. Or, to put it otherwise, there might easily be, somewhere in Canada, near our borders, a mine so favored that its product could be profitably

Jan 1, 1892

By Terkel Rosenqvist

Few subjects in iron metallurgy and steelmaking have caused so much discussion and have resulted in so many divergent and partly contradictory statements as the theory of the distribution of sulphur between molten iron and slag. An interesting survey of the different points of view is given by Grant and Chipman.1 Grant and Chipman themselves conclude in their paper that, at least in the open hearth and electric steel furnaces, the governing reaction is a simple distribution like: FeS steel ? FeS alas [Ia] and MnS steel ? MnS alas [Ib] They conclude that no significant reaction takes place according to the more classical scheme: FeS steel + CaO slag ? FeOslag + CaS slag [2a] This is the reaction which is regarded by most investigators as the primary sulphur reaction in the blast furnaces, where it is accompanied by the reaction with carbon: FeO slag + C ? Fe + CO [2b] The writer suggests an alternative to the reactions mentioned above. It is the opinion of the writer that the a priori assumption of defined molecular compounds being present in molten steel as well as in molten slag, has retarded rather than promoted a solution of the sulphur problem. As for the constituents of molten steel, it is taking too much for granted to mention the presence of FeS and MnS. If this infers that the melt contains diatomic molecules, the statement must be made that at least such molecules do not exist in the solid state at room temperature. Solid FeS crystallizes in the nickel-arsenide structure, and MnS (high temperature form) in the sodium-chloride structure. In these structures the sulphur is surrounded by six metal neighbors, and no molecular groups can be isolated. When sulphur is dissolved in molten steel, it is expected to maintain the same coordination number as in the solid state. We know that sulphur in steel has a certain chemical potential and a chemical activity which can be expressed by the reaction: S steel + H2 ? H2S where the activity A. is proportional to the ratio PH2S/Ph2. We know also that this activity is influenced by the presence of other constituents. For instance, there is reason to assume that carbon and silicon increase the sulphur activity and manganese decreases it. However, the exact relationship here is scarcely known, and further investigations are needed. Concerning the molten slags, if anything should be assumed a priori it would be that they are composed of ionic rather than molecular parts. There are indications of this in that solid silicates form ionic structures, and molten slags show high electric conductivity and can be electrolyzed.2 It has been claimed by Taylor and Chipman3 that their activity investigations

Jan 1, 1949

By Terkel Rosenqvist

Few subjects in iron metallurgy and steelmaking have caused so much discussion and have resulted in so many divergent and partly contradictory statements as the theory of the distribution of sulphur between molten iron and slag. An interesting survey of the different points of view is given by Grant and Chipman.1 Grant and Chipman themselves conclude in their paper that, at least in the open hearth and electric steel furnaces, the governing reaction is a simple distribution like: FeS steel ? FeS alas [Ia] and MnS steel ? MnS alas [Ib] They conclude that no significant reaction takes place according to the more classical scheme: FeS steel + CaO slag ? FeOslag + CaS slag [2a] This is the reaction which is regarded by most investigators as the primary sulphur reaction in the blast furnaces, where it is accompanied by the reaction with carbon: FeO slag + C ? Fe + CO [2b] The writer suggests an alternative to the reactions mentioned above. It is the opinion of the writer that the a priori assumption of defined molecular compounds being present in molten steel as well as in molten slag, has retarded rather than promoted a solution of the sulphur problem. As for the constituents of molten steel, it is taking too much for granted to mention the presence of FeS and MnS. If this infers that the melt contains diatomic molecules, the statement must be made that at least such molecules do not exist in the solid state at room temperature. Solid FeS crystallizes in the nickel-arsenide structure, and MnS (high temperature form) in the sodium-chloride structure. In these structures the sulphur is surrounded by six metal neighbors, and no molecular groups can be isolated. When sulphur is dissolved in molten steel, it is expected to maintain the same coordination number as in the solid state. We know that sulphur in steel has a certain chemical potential and a chemical activity which can be expressed by the reaction: S steel + H2 ? H2S where the activity A. is proportional to the ratio PH2S/Ph2. We know also that this activity is influenced by the presence of other constituents. For instance, there is reason to assume that carbon and silicon increase the sulphur activity and manganese decreases it. However, the exact relationship here is scarcely known, and further investigations are needed. Concerning the molten slags, if anything should be assumed a priori it would be that they are composed of ionic rather than molecular parts. There are indications of this in that solid silicates form ionic structures, and molten slags show high electric conductivity and can be electrolyzed.2 It has been claimed by Taylor and Chipman3 that their activity investigations

Jan 1, 1949

The performance of a two-horizon depletion-type reservoir produced through combination wells is analyzed. By introducing some simplifying approximations, it has been possible to obtain formulas which are easy to handle. Only ordinary differential equations are used, and the development of the analysis can be followed without difficulty by the non-specialist. A rigorous analysis has been made of this problem. It has been found that the approximations introduced in the simplified analysis are fully justified and that errors seldom will be more than 2 per cent. The report shows the effect of the rate of withdrawal upon the relative depletion of the two horizons. Numerical examples are given. INTRODUCTION In its simplest form an oil reservoir consists of a continuous, homogeneous body of porous and permeable rock, enclosed at the top and the bottom by impermeable material. The flow of fluid through such a reservoir has been the subject of numerous papers, and the mathematical analysis of well performance, pressure build-up, etc., has reached a high degree of refinement. One of the basic assump tions introduced into these analyses is the homogeneity of the reservoir. In non-homogeneous reservoirs, these computations still can be carried out satisfactorily, provided small irregularities in the physical properties of the rock are distributed in a random fashion. The flow equations are derived as solutions of the continuity equation, and their solutions are dependent upon the assumption of many constant factors in the reservoir: permeability to oil, compressibility of the reservoir fluid, viscosity saturation, etc. When these axe assumed to be constant, the continuity equation can be solved rigorously. When these assumptions do not hold and corrections are introduced, it becomes very difficult and often impossible to solve analytically. The present analysis is concerned with production from a two-layer depletion-type reservoir in which the layers have different permeabilities. Instead of using the continuity equation, results were derived from some simple physical ideas. In a single-layer reservoir in which the oil is at a pressure above the bubble point, the rate of production often has been assumed to be directly proportional to the pressure drawdown. In the simplified analysis it has also been assumed that the drop in average reservoir pressure is directly proportional with the cumulative withdrawal. These considerations in the past have been the basis of the analysis of reservoir performance and have been applied to a variety of problems, often with marked success. In the problem under investigation these relationships are shown to be compatible with the equation of continuity, but the approach has the advantage of leading to ordinary differential equations in which changes in constants can be introduced without making the analytical solution impossible. It has the additional advantage that it can be understood more readily by the large group of engineers who are not reservoir specialists. For that reason, detailed steps in the mathematical developments have been shown in full. SCOPE OF ANALYSIS The analysis in this paper has been applied to a two-layer depletion-type reservoir in which both horizons are produced simultaneously in the same well. Because of the difference in permeability, it is obvious that the depletion of the two zones will proceed at different rates. For various problems it may be of interest to know the degree of depletion of the two zones at any arbitrary time and to in-

By N. J. Grant, C. Stein

A more complete determination of the chromium-rich portion of the Cr-Ni phase diagram was made, based in part on resistivity measurements. The existence of a eutectoid reaction at 1215°C,made,based in addition to the previously reported eutectic reaction at 1343°C, was confirmed. Metallographic studies, lineal analysis, and diffusion-couple evidence were utilized to support Metallographicand extend the findings of the resistivity measurements. Delineation of the a chromium solvus line shows that the maximum solubility of nickel in a chromium decreases rapidly from 25 wt pct Ni at the eutectoid temperature to 16 wt pct. Ni at 950°C. IN recent years alloys of high chromium and nickel content have become of more interest as better performance of metals at higher temperatures is sought. It has become increasingly important, therefore, that the Cr-Ni binary diagram, which is composed of two of the elements commonly found in many high temperature alloys, be known more accurately. In particular, the chromium-rich portion of this diagram has for a long time remained incompletely determined and has been reported in the literature with a great deal of conflicting evidence. In general, electrolytic chromium of nominal purity was used by most of the earlier workers, who, except for Jenkins et al., made no further attempt to purify the metal. In the present redetermination of the chromium-rich portion of the Cr-Ni phase diagram, every effort was made to use the purest component metals available and to retain this purity throughout the preparation of the alloys and their subsequent handling. Early work by Voss, Bain," and Phebus and Blake4 indicated that the Ni-Cr binary diagram was a simple eutectic system with rather extensive terminal solid solutions. Later, Nishigori and Hamasumi," Tasaki, Weaver and Jellinghaus,' Matsunaga, and Jette, Nordstrom, Queneau, and Foote attempted to determine the limits of the phase fields. Except for Jette and coworkers, the other investigators agreed that the temperature of the eutectic reaction occurred between 1320" and 1340°C and at a composition of 50 or 51 pct Cr. There was, however, considerable disagreement as to the melting point of the chromium-rich alloys and the limits of the solid-solution fields. As a result of the studies of Jenkins et al., the liquidus and solidus curves up to 80 and 90 pct Cr, respectively, were outlined. In addition, the solid-solution phase fields at higher temperatures had been investigated and showed only two phases. The boundary of the chromium-rich a phase was not determined precisely according to these authors, but indications were that it tended to confirm the earlier work of Nishigori and Hamasumi. A more recent investigation by Taylor and Floyd,'" using X-ray methods, essentially corroborated the diagrams proposed by Jenkins et al., and by Wise and Eash (see Fig. 1). Again, no indication of a third phase in the chromium-rich portion of the diagram appeared. The earlier observations, however, are not substantiated by the modifications to the Ni-Cr binary diagram proposed by Bloom and Grant." In the investigation carried out by Bloom and Grant, X-ray methods showed that an eutectoid reaction existed at approximately 1180°C, in addition to the eutectic reaction at 1343°C (see Fig. 1). Their determination of the melting point of pure chromium was 1930°C (later revised to 1903"C)." Experimental Procedure and Results The chromium used for this study was electrolytic chromium, made available by the United States

Jan 1, 1956

Jan 1, 1927